(57) A catheter balloon is prepared for inflation, and the balloon is inflated by the following process. At least a portion of an elastic, thermoplastic tube is radially stretched until the radially stretched tube portion exhibits a desired increase in molecular orientation. The stretching conditions, such as selective heating, preferably cause a central section of the stretched tube portion to have less wall thickness than end sections of the tube portion. At least part of the tube portion may be longitudinally stretched relative to the tube, to create a desired biaxial molecular orientation. Thereafter, the tube portion is optionally placed into a stent, the tube portion being part of a catheter. The tube portion is inserted into a patient to position the stent and tube portion at a desired position, such as a location in the coronary artery. After positioning of the tube portion and stent, the lumen of the tube portion is pressurized to cause radial expansion of the tube portion within the patient, with a central section of the tube portion expanding first.